PERCENTAGE. 255. PER CENT. means by the hundred. Thus, 1 per cent. of a number is one-hundredth of it; 2 per cent. is two-hundredths of it; 3 per cent. three-hundredths, &c. 256. The RATE PER CENT. is the number of hundredths taken.. Thus, if 1 hundredth is taken, the rate is 1 per cent.; if 2 hundredths are taken, the rate is 2 per cent.; if 3 hundredths, the rate is 3 per cent., &c. 257. The BASE is the number whose part is taken. 258. The PERCENTAGE is the result of the operation, and is the part of the base takeň. The rate per cent. is generally expressed decimally; thus, .8 per cent. of a number, is 8% of it = .0085 of it. NOTE. Per cent. is often expressed by the character %. Thus 5 per cent. is written 5%; 8 per cent., 8%. Write, decimally, 5%; 8%; 15%; 100%; 204%; 3271% 672.3%; 49%; and 507.5%. 255. What is the meaning of per cent.? What is 5 hundredths of a number?--256. What is the rate per cent.? If four hundredths of a number is taken, what is the rate?-257. What is the base?-258. What is the percentage? How is the rate per cent. generally ex pressed? 259. To find the percentage, when the base and rate are known. 1. What is the percentage of $450, the rate being 6 per cent.? ANALYSIS. The rate, expressed decimally, is 06. The percentage is, therefore, six hundredths of the base, or the product of the base and rate. Hence, to find the percentage of any number: OPERATION 450 .06 $27.00 Ans Rule.-Multiply the base by the rate, and the product will be the percentage. Examples. Find the percentage of the following numbers: 1. 4 per cent. of $1256. 2. 12% of $956.50. 3. per cent. of 475 yards. 4. 7% of 324.5 cwt. 8 5. % of 125.25 lbs. 8. 9 per cent. of 186 miles. 9. 103 per cent. of 460 sheep. 10. 5 per cent. of 540 tons. 11. 8 per cent. of $3465.75. 12. 12% of 126 cows. 16. 105 per cent. of 2500 bar. 23. What is the difference between 43% of $1000 and 71⁄2 per cent. of $1500? 24. If I buy 895 gallons of molasses, and lose 17 per cent. by leakage, how much have I left? 25. A grocer purchased 250 boxes of oranges, and found tha he had lost in bad ones 18 per cent.: how many full boxes good ones had he left? 259. How do you find the percentage from the base and rate? 260. Parts of percentage. There are three parts in percentage: 1st. The Base; 2d. The Rate; and 3d. The Percentage. 261. To find the rate, when the base and percentage are known. 1. What per cent. of $64 is $16? or, $16 is what part of $64? OPERATION. 18= = .25, or 25 per cent. ANALYSIS. In this example, 16 is the percentage, and 64 the base, and the rate is required. Since the percentage is equal to the base multiplied by the rate, the rate is equal to the quotient of the percentage divided by the base. Rule.-Divide the percentage by the base, and the first two decimal places will express the rate. Examples. 1. What per cent. of 10 dollars is 2 dollars? 3. What per cent. of 40 pounds is 3 pounds? 4. Seventeen bushels is what per cent. of 125 bushels? 5. Thirty-six tons is what per cent. of 144 tons ? 6. What per cent. is $84 of $96 ? 7. What per cent. is of ? 8. What per cent. is 3 miles of 400 miles? 9. Four and one-third is what per cent. of 9? 10. One hundred and four sheep is what per cent. of a drove of 312 sheep? 11. A grocer has $325, and purchases sugar to the amount of $121.87 what per cent. of his money does he expend? 12. Out of a bin containing 450 bushels of oats, 561 bushels were sold what per cent. is this of the whole? NOTE. If the base be regarded as a single thing, and denoted by 1, a fractional percentage expressed decimally will denote the rate. 260. How many parts are there in percentage? What are they? 261. How do you find the rate, from the base and percentage? 13. of a number is what per cent. of the number? 14. of a ship is what per cent. of the ship? 15. of 50 is what per cent. of 50? 16. of a cargo is what per cent. of it? 17. 13 times a number is what per cent. of the number? 262. To find the base, when the rate and percentage are known. 1. Of what number is $960, 16 per cent.? ANALYSIS.-By Art. 259, the percentage is equal to the base multiplied by the rate; hence, to find the base, OPERATION. 960.16 6000 Rule.-Divide the percentage by the rate, expressed deci mally. Examples. 2. The number 475 is 25% of what number? 3. The number 87 is 12% of what number? 4. Five hundred and sixty dollars is 140% of what number? 5. The number 75 is % of what number? 6. One dollar and twenty-five cents is 7% of what number? 7. The fraction is 45% of what number? 8. The fraction is 5% of what number? 9 If a person receives $5850, and that sum is 75% of what is due him, what is, the debt? 10. A bankrupt can pay only 37 per cent. of his debts: what did he owe to that merchant to whom he paid $1647 ? 11. In an army, 15600 men are mustered after a battle, in which 25% were killed and wounded: what was the original number of men? 263. AMOUNT is the percentage plus the base. 264. DIFFERENCE is the percentage minus the base. 262. How do you find the base, when the rate and percentage are known?-263. What is the amount?-264. What is the difference? 265. Knowing the amount and rate, to find the base. 1. Mr. Jones buys 8 hogsheads of sugar, sells them at an advance of 15 per cent., and receives $170 what did he pay for the sugar? ANALYSIS. The amount received, $470, arises from adding the percentage to the base; that is, it arises from multiplying the base by 1 plus the rate per cent.; hence, to find the base, OPERATION. 1.15)470(400 Rule.-Divide the amount by 1 plus the rate, expressed decimally. Examples. 1. What number is that, to which if 1 per cent. of it be added, the sum will be 392 ? 2. What was the population of a city in 1850, which increased 15 per cent., and in 1860 contained a population of 10350? 3. A farmer bought a flock of sheep, which in three years increased 96 per cent., and then numbered 1078: how many did he buy? 4. Mr. Jones sold his farm for $1008, which was thirtythree and one-t e-third per cent. more than he gave for it: what did it cost him? 5. A man bought a horse and cow; he paid for the horse one hundred and twenty-two dollars, which was three hundred and five per cent. more than he paid for the cow how much did the cow cost him? NOTE. If the rate per cent. exceeds one hundred, the whole number, to which the rate is added, must be increased 1 for each hundred. 65. How do you find the base, when the amount and rate are wn? |